On some algebraic properties and applications of polynomial dynamics over finite fields

Alina Ostafe (University of New South Wales)

Thursday, 10 July 2014, 15:00, b-it 1.25 (cosec meeting room)

Algebraic Dynamical Systems over finite fields, that is, dynamical systems generated by iterations of polynomials and rational functions, are exciting and challenging mathematical objects with intricate algebraic and number theoretic properties and very complex behaviour. Controlling algebraic properties of iterates is a fundamental mathematical problem whose solution has multiple implications, but little progress has been made in this direction.

In this talk I will outline some algebraic and number theoretic properties of such dynamical systems which include: degree growth, representation of iterates, irreducibility and irreducible divisors of polynomial iterates. We note that only few results are known and many questions remain wide open.